In order to utilize the superb electronic properties of graphene in future electronic nano-devices, a dependable means of controlling the transport properties of its Dirac electrons has to be devised by forming a tunable band gap. We report on the ion-induced modification of the electronic properties of single-layer graphene (SLG) grown on a SiC(0001) substrate by doping low-energy (5 eV) Li(+) ions. We find the opening of a sizable and tunable band gap up to 0.85 eV, which depends on the Li(+) ion dose as well as the following thermal treatment, and is the largest band gap in the π-band of SLG by any means reported so far. Our Li 1s core-level data together with the valence band suggest that Li(+) ions do not intercalate below the topmost graphene layer, but cause a significant charge asymmetry between the carbon sublattices of SLG to drive the opening of the band gap. We thus provide a route to producing a tunable graphene band gap by doping Li(+) ions, which may play a pivotal role in the utilization of graphene in future graphene-based electronic nano-devices.